Question

In a system of two particles of masses \(m_1\) and \(m_2\), the second particle is moved by a distance \(d\) towards the centre of mass. To keep the centre of mass unchanged, the first particle will have to be moved by a distance

• A. \( \dfrac{m_1}{m_2} d \), towards the centre of mass
• B. \( \dfrac{m_2}{m_1} d \), away from the centre of mass
• C. \( \dfrac{m_2}{m_1} d \), towards the centre of mass
• D. \( \dfrac{m_1}{m_2} d \), away from the centre of mass

Hint:

To keep centre of mass fixed, mass–displacement products must balance each other.

Answer 1

The Correct Option is C

Step 1: Write the condition for centre of mass.
For two particles, the position of centre of mass is given by \[ m_1 x_1 + m_2 x_2 = \text{constant} \]

Step 2: Apply displacement condition.
If the second particle moves a distance \(d\) towards the centre of mass, its displacement is \(-d\). Let the displacement of the first particle be \(x\) towards the centre of mass.

Step 3: Apply conservation of centre of mass.
\[ m_1 x + m_2(-d) = 0 \] \[ x = \frac{m_2}{m_1} d \]

Step 4: Direction of motion.
The positive value indicates that the first particle must move towards the centre of mass.